If-and-only-if-it expresses biconditional logical connective between two statements. In the construction Something is ... if-and-only-if-it ... equivalent concepts are introduced. The concequent concept can be a complex concept. It allows to define new concept as intersection, union etc. of old ones. The construction can me modified to give complement concept.


Those examples show how to define concepts.

Example: Equivalent concepts.
Something is a boy if-and-only-if-it is a young-male-man.
Example: Concept intersection.
Something is a young-male-man if-and-only-if-it is a young-thing and is a male-thing and is a person.
Example: Everything in the world is an adult-thing or a young-thing. The concepts are complement.
Something is a young-thing if-and-only-if-it is not an adult-thing.